Chapter 1.6, Problem 34E

(a)

To determine

To Explain: The natural logarithmic function.

Explanation of Solution

The natural logarithmic function is denoted as ln x which equals the logarithmic function with base e.

That is, ${\log }_a\left(x\right)=\ln \left(x\right)$ where e is a constant or Euler’s number $e\approx 2.71828183$.

(b)

To determine

To Explain: The common logarithmic function.

Explanation of Solution

A logarithm with base 10 is said to be a common logarithm which is defined as, ${\log }_{10}\left(x\right)$

(c)

To determine

To sketch: The graphs of the natural logarithm function and the nature exponential function in a common plane.

Explanation of Solution

Graph:

The natural logarithm function is, $y=\ln x$ and the nature exponential function is, $y=e^x$.

Use online graphing calculator and obtain the graphs of the functions $y=\ln x$ and $y=e^x$ as shown in the Figure1.

From Figure1, it is observed that the graphs are reflection of each other about the line $y=x$.